Refractory erosion due to fluid flow is caused by the shear stresses acting on the liquid/solid interface. This mechanism of continuous wear has not been extensively investigated based on appropriate physical considerations. This study proposes a novel method for the inverse calculation of erosion parameters in slag-refractory systems. A computational fluid dynamic model is coupled with optimisation software to solve a nonlinear least-squares problem for the identification of erosion parameters from experimental erosion profiles. Erosion-rate modelling is performed based on a three-parameter law of the acting shear stress. A test problem is studied using artificially generated erosion profiles. The feasibility of the approach with two parameters is proven; however, using three parameters causes the problem to become ill-posed. Moreover, the method is successfully applied to a real experiment with an alumina coarse-grain refractory. Statistical analysis of the solutions is performed for both the test problem and real experimental profile. Confidence intervals and regions calculated via linearisation are examined, but their use is limited and should be evaluated for each case. This method can serve as a basis for further investigations concerning the quantification of refractory erosion.